The stiffness of an inner toothed ring in an epicyclic gear is usually considered in combination with the stiffness of the teeth of the ring. Thus, any significant deviation from an ideal tooth geometry substantially increases the load on the surrounding ring material in proportion to the stiffness of the ring. For a conventional inner toothed ring of the type used in epicyclic gear trains, efforts to reduce stiffness of the ring are limited by the resultant material stress levels in the ring.